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Post #878 (isolation #1) » Sun Aug 02, 2020 8:58 pm
Postby Sirius9121 »
at least 1/2 of the digits of n^2-1 are the same number and the repeating number is a number that is shown on the middle or right hand side of a keypad
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Post #892 (isolation #6) » Mon Aug 03, 2020 1:41 pm
Postby Sirius9121 »
Play 24, 2, 43, 15, 256, 4, 20 as: at least 1/2 of the digits of n^2-1 are the same number and the repeating number is a number that is shown on the middle or right hand side of a keypad
I think, without doing the math, that it meets the "rarer than every card is even" criteria.
I cannot tell without doing the math whether it meets the meta rule or not? How often can we get a bingo by following an algorithm like "the numbers (mod n) fit into a range of < n/2 "?
4 options in mod 14 =
0.155% of bingo
def meet req./
I think that it should be allowed, due to the fact that:
1. It's much more creative than cutoffs like (3 to 27)
2. It's very rare
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Post #917 (isolation #16) » Wed Aug 05, 2020 3:36 am
Postby Sirius9121 »
(changed)
x is a composite number where
x^3's first digit is in the sequenct T(n)=2^n
x^4's last digit squared's last digit is the same
x^5's first digit is in the sequence T(n) = T(n-1) + 2^(n-2)
x^6's first digit is not a composite number
In base 8, at least 50% of the numbers are a same repeating digit and the repeating digit is a square of any non-negative integer (0,1,4)
I think this meets all the criteria. Does anyone have any objections to this bingo in particular?
--
More broadly, assuming sirius tries to get a bingo every turn for the rest of the game, is this going to impact everybody's enjoyment of the game and what can we do to ensure that everybody has a good time? I think in future games, bingos should be worth fewer points, to start with.
It's also important to me that we be welcoming to any players who are prone to being intimidated by math. Math at any level, whether you're trying to learn how to multiply or trying to prove the twin prime conjecture, can feel a lot like this:
I want to encourage everyone to play with numbers and draw connections between them, however silly and spurious.
I want it to be safe to draw owls that look like
I'm willing to do the following measures to keep the game fun:
Bingos are worth 10 points for (me only), not including ones I submit for teammates, however if someone has more points than my team I get 14 instead of 10.
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Post #939 (isolation #24) » Thu Aug 06, 2020 3:05 pm
Postby Sirius9121 »
@Plotinus:
Idea:
Consider a scale of 'highest point score' and 'lowest point score' on 0 - 100
If you are on the 0 - 25th percentile, you score 14.
.... 25 - 75, you score 12.
.... 75 - 100, you score 10.
example for now:
7:24:0
so 24 = 100x + 0
7 is on the 29th percentile on 0 to 24, so they get 12 points per bingo.
24 is on the 100th percentile on 0 to 24, so they get 10 points per bingo.
0 is on the ... 0th percentile on 0 to 24, so they get 14 points per bingo.
But the point count is for the moment they submitted the bingo, so our team's first bingo would be worth... 0 is on the undefined percentile?
So imo the first bingo would be 14 points
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Post #960 (isolation #29) » Tue Aug 11, 2020 5:30 am
Postby Sirius9121 »
Play what you are strong at.
*i have backup move(s) ready in case you cant, but im not going to use them until nessecary! Hope you can try it by yourself!
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Post #982 (isolation #34) » Sat Aug 15, 2020 3:36 am
Postby Sirius9121 »
digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
= digit sum is 1/3/6/8/13
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Post #1023 (isolation #42) » Wed Aug 26, 2020 11:34 pm
Postby Sirius9121 »
Nancy, Haversine seems to be catching up. If you don't have any repeating numbers in your hand, I kinda suggest to post it, we seem to really need a bingo rn
In post 1023, Sirius9121 wrote:Nancy, Haversine seems to be catching up. If you don't have any repeating numbers in your hand, I kinda suggest to post it, we seem to really need a bingo rn
2, 14, 64, 35, 2, 144, 56,
Okay, I guess it doesn’t hurt to take a shot. *screaming internally*
2227222
Each number contains either the exact number or a multiple of either 2 or 7 and twice, both of them.
[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n2 - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2
i
× 3
j
× 5
k
for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] In base 8, at least 50% of the numbers are a same repeating digit and the repeating digit is a square of any non-negative integer (0,1,4)
[14, 15, 5, 57, 81, 19, 60] the first number of x is a term of 'a(n) is the largest term in the continued fraction for a(n-1) + n^2/a(n-1), where a(1)=1.'
[69, 529, 14, 15, 28, 45, 92, 1000] “integer multiples of the jersey numbers from the starters on the Los Angeles Lakers in their game on August 13” (those jersey numbers are 23, 88, 5, 7, and 14)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
Haversine: vincentw, ErrantParabola: 29 points
[9, 73, 90, 7] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[62, 97, 68] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[841, 576, 36] {
n2
}square numbers
Exsecant: Sirius9121, Nancy Drew 39: 44 points
[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
Chord: StrangerCoug, D3f3nd3r: 22 points
[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[11, 32, 34] Numbers whose digit sum is prime
Haversine gains 7 points.
It is
Sirius*******1921********
's turn.
Siriuis has submitted his turn by PM
[34, 400, 9, 15, 27, 87, 53] as x2's first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
There are exactly 50 such numbers in between 1 and 100 inclusive. Complaints? Quibbles?
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Post #1048 (isolation #50) » Sun Aug 30, 2020 10:34 pm
Postby Sirius9121 »
In post 1044, Plotinus wrote:I think I am too. He included this screenshot, and clarified that it means that x2 starts with 1, 2, 7, or 8
As for the rest though, I think it means:
There is only one seven digit number that is palindromic in base 1 and it's palindromic in base 2 as well 11111111 = 1012 = 710
Numbers that are palindromic in base 2: 10000012 = 21023, 10010012 = 22013 , 10101012 = 100113, 10111012 = 101103, 11000112 = 102003, 11101112 = 111023, 11111112 = 112013, so there are no such numbers that are also palindromic in base 3.
If I look up this sequence in the OEIS, I find https://oeis.org/A308918, which is worded exactly as Sirius worded it. It looks like the sequence is increasing, but do we know that it will always increase, that we'll never find a large base that has only a small number that fits this pattern?
Also, if your meta algorithm is to look up four single-digit numbers in the OEIS then this algorithm generates a bingo 100% of the time, which is 63/64 too many.
tbh i have done a project (?) on palindromic numbers before so I remember this sequence from memory.
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Post #1055 (isolation #52) » Mon Aug 31, 2020 12:38 pm
Postby Sirius9121 »
In post 1051, D3f3nd3r wrote:Your team still has a multiple-bingo lead though and had as many points as both of our teams combined until the last turn, “catching up” seems like a bit of a stretch
Haversine has more than half of our points. Considering my handicap it's a lot